The quantum computer is a computer that is overwhelmingly high in the speed of computation in solving those specific problems which are virtually impossible to compute with classical computers. It uses units in a quantum two level system called quantum bits corresponding to bits used in the classical computer. While the quantum computer uses a large number of quantum bits in computation, it is basically operated by a quantum processor device that performs unitary transformation for any given quantum bit and reads out the quantum bit after the transformation.
An explanation is given of basic particulars by taking a spin as an example. In general, applying a static magnetic field to a spin having a quantum number of ½ allows the spin to take one of two states that it is oriented parallel (upwards) and anti-parallel (downwards) to the applied static magnetic field, namely |0> or |1>, or further a state that it is inclined to the magnetic field. This latter state is a state of superposition of the upward state |0> and the downward state |1> and is described by equation (1) as follows:|s>=α|0>+β|1>  (1)where α and β are complex numbers which satisfy equation (2) as follows:|α|2+|β|2=1  (2)With the spin orientation measured, the state |s> brings about a change called “convergence of wave packet” to become either the state |0> or the state |1>. Then, the probabilities that the result of measurement is the state |0> and the state |1> are given as |α|2 and |β|2, respectively. Innumerable states are possible which even if they give an identical probability in their measurement result, namely the |α|2 or |β|2 that is identical, are different in α or β, and they are distinguished from one another by their “phases”.
A state of superposition given by equation (1) functions as a quantum bit. To wit, while the classical bit is simply either 0 or 1 state, the quantum bit is not simply either state |0>(|α|2=1, |β|2=0) or state |1>(|α|2=0, |β|2=1). In addition to these two states (|0>and |1>), there exist innumerable states |s> intermediate between them (in which neither |α|2 nor |β|2 is 1 or 0) and further innumerable states |s'> also varying in phase. Changing or transforming one state |s> to another state |s'> by some operation is called unitary transformation.
In general, constructing a quantum computer requires providing it with four functions as follows: First is initialization. That is, a mean must be provided that initializes the initial state of a quantum bit to a well defined state, e.g., to |0>or |1>.
Second is a means for controlling the state (quantum processing gate). That is, a means must be provided for the unitary transformation of a prepared initial state (e.g., |0> or |1>) to any state of superposition |s> as desired. This latently includes the requirement that the spin state may not be disturbed and the phase may not be lost (made decoherent) affected by the environment.
Third is: read-out. That is, a means must be provided that measures a state |s> after the unitary transformation, or determines the value of a |α|2 or |β|2.
Fourth is expandability. In the first place is there required a conditional state control (controlled not gate) for two bits, which must then be expanded by integration for a number of quantum bits.
The present invention contemplates providing a quantum processor device equipped with the first to third of the four functions above. Thus, quantum processor devices according to the present invention when used do not immediately allow making up a quantum computer, but they are components necessary and essential in the makeup of such a quantum computer.
Mention is next made of basic particulars about a method of the unitary transformation of one bit. If a nuclear spin is used to serve as a quantum bit, then its polarization (orientation) is designated as a state |s> in equation (1). To wit, if it is oriented upwards, the |α|2=1 and |β|2=0 in equation (1). If it is oriented downwards, the |α|2=0 and |β|2=1 in equation (1). A polarized state in which the spin is inclined is defined by designating α and β having values other than them. Energy E0 of state |0> that is parallel to magnetic field is lower than energy E1 of state |1> that is antiparallel to magnetic field. Frequency f that is equal (or proportional) to difference between energy E1 and energy E0 as follows:hf=E1−E0  (3)where h is Planck's constant is referred to as NMR (Nuclear Magnetic Resonance) frequency. If the initial state is |0>, applying an oscillating magnetic field having a NMR frequency to a static magnetic field perpendicularly thereto causes the spin state to be unitary-transformed in general with time t and its evolution with time is expressed as α and β in equation (1) changing with time as shown by equations (4) and (5) below,|α(t)|2=cos 22πFΔt)  (4)|β(t)2=sin 2(2πFΔt)  (5)where F is a constant that is proportional to the amplitude of the applied oscillating magnetic field. The unitary transformation of a nuclear spin state is executed by applying an oscillating magnetic field in the form of a pulse. Thus, applying an oscillating magnetic field pulse having a pulse width Δt gives a state after the application |s>=α|0>+β|1>, where it is transformed into:|α|2=cos 2(2πFΔt)  (6)|β|2=sin 2(2πFΔt)  (7)
FIG. 6 is a conceptual view showing a typical in-solid nuclear spin processor device theoretically proposed and utilizing a single in-solid nuclear spin when controlled. See Nature, Vol. 393, p. 133 (1998).
In the example shown there, a structure having phosphor (31P) 602 disposed in silicon 601 is provided with a metallic gate 604 via a barrier 603. With silicon (28Si) having no nuclear spin, the nuclear spin with the quantum number of ½which phosphor has functions as a quantum bit. Where silicon is tetravalent while phosphor is pentavalent, applying a bias voltage to the metallic gate 604 allows the extra charge which the phosphor possesses to be brought away from and near to the atomic nucleus. This in turn allows strengthening and weakening the hyperfine interaction between the electron spin and the nuclear spin. As a result, it is possible for the resonance frequency of nuclear magnetic resonance being described below to be controlled with a gate voltage. Further, although not shown, arranging a number of such structures adjacent one to next in a row allows forming a number of such quantum bits and connecting them together.
In this prior theoretical proposal of an in-solid nuclear spin processor device, NMR is brought about by a pulsed radiofrequency magnetic field to control the nuclear spin state |s> whereby the operation of its unitary transformation is effected as mentioned above to process quantum bits.
In a quantum computer having a makeup as mentioned above, the need to make a device smaller in size while achieving a high speed of its operation imposes the requirement on the device that each state of each of nuclear spins which must be as smaller as possible therein be controlled and read out at even a higher speed. The abovementioned theoretical proposal involves problems such as the need to completely remove impurities out of a silicon crystal, a technique of implanting precisely at a given location therein with a 31P ion and micromachining at a precision in the order of 0.05 micrometer, all of which appear to be impossible to solve by the existing semiconductor technologies.
On the other hand, FIG. 7 shows in a conceptual view an exemplary device using a quantum Hall edge state achieved by a two dimensional electronic system in a semiconductor placed at a very low temperature and in a high magnetic field and wherein for a group of nuclear spins their polarizations are read out. See Physical Review B, Vol. 56, p. 4743 (1997). In this example, a semiconductor hetero structure 701 is formed with electrodes 702 and a metallic gate 703. Passing a radiofrequency current through a coil 704 to impart a radiofrequency magnetic field modulation to the semiconductor hetero structure allows the nuclear spins to be detected.
In this device, however, the coil that generates the radiofrequency magnetic field to bring about nuclear magnetic resonance is several millimeters in diameter, much larger in size than a limited region in the order of several micrometers where the spin state (quantum bit) is to be detected. This may cause the entire two dimensional electronic system, the electrodes and the lead wires to be heated and the quantum Hall effect to collapse, preventing the nuclear spin from being controlled at high speed. The device has also the difficulty that the spin control has to be effected simultaneously for the nuclear spins existing in the entire two dimensional electronic system.
Thus, the prior in-solid nuclear spin quantum processor devices by theoretical proposals have been found either impossible to manufacture because of the need for a semiconductor microstructure that cannot be realized in the existing level of technologies or to fail to allow only a limited number of spins to be controlled and read out.